Non Lipschitz triangular canonical form for uniformly observable controlled systems

We study the problem of designing observers for controlled systems which are uniformly observable and differentially observable, but with an order larger than the system state dimension : we have only an injection, and not a diffeomorphism. We establish that they can be transformed into a triangular canonical form but with possibly non locally Lipschitz functions. Since the classical high gain observer is no longer sufficient, we review and propose other observers to deal with such systems, such as a cascade of homogeneous observers.